expected_value.py

from random import random
from statistics import mean

variables = [3, 5, 7, 10, 12, 13]
weight = [.1, .05, .05, .2, .4, .2]

if sum(weight) != 1:
    raise 'sum(weight) != 1'

range_of_weight = [sum(weight[0:index + 1]) for index, w in enumerate(weight)]


def get_random_variable():
    random_number = random()
    selected = None
    for index, w in enumerate(range_of_weight):
        if random_number <= w:
            return variables[index]


exact_expected_value = sum([w * v for w, v in zip(weight, variables)])
print('exact_expected_value', exact_expected_value)

average_expected_value = mean([get_random_variable() for _ in range(1000000)])
print('average_expected_value', average_expected_value)